Three vectors `vecA=ahati+hatj+hatk, vecB=hati+bhatj+hatk and vecC=hati+hatj+chatk` are mutually perpendicular `(hati,hatj and hatk` are unit vectors along X, Y, and Z axis respectively).
The respective values of a,b and c are

Options

A. 0,0,0
B. `-(1)/(2),-(1)/(2),-(1)/(2)`
C. `1,-1,1`
D. `(1)/(2),(1)/(2),(1)/(2)`

Answer

B

Explanation

Here `vecA=(ahati+hatj+hatk)`
`vecB=(hati+bhatj+hatk)` and `vecC = (hati+hatj+chatk)` are mutually perpendicular ,
`:. vecA.vecB=0 ` i.e , a+b+1=0
`vecB.vecC=0` i.e., 1+b+c=0
`vecC.vecA=0` i.e., a+1+c=0
From eqn. (i) ,(ii) and (iii)
`a=-(1)/(2) ,b =-(1)/(2),c=-(1)/(2)`